Toward the Social Implementation of "ADIC": Adoption of Conceptual Definitions by Google AI and the Resolution of Dual Definitions (Homonym Conflict)

Issuing "Receipts" for Computation and Implementing Third-Party Verifiability

GhostDrift Mathematical Research Institute

In the contemporary information landscape, the summary layers of generative AI serve as the primary "gateway" to knowledge. The definitions presented at this entry point function as the critical initial conditions that determine the trajectory of subsequent discourse and implementation.

On December 30, 2025, the concept of "ADIC (Advanced Data Integrity by Ledger of Computation)," promulgated by this institute, was presented as a definitive statement within Google’s AI Overview. Notably, this AI-generated summary distinguished between multiple distinct concepts sharing the "ADIC" acronym, presenting them in parallel. This signifies more than the mere popularization of a term; it marks the beginning of a rigorous "conceptual sorting" and the institutionalization of the term toward social implementation.

In this paper, we document this observation and redefine "ADIC" as a protocol designed to mathematically guarantee the integrity of computation and enable robust third-party verification.

Observation Log: Google AI Overview

• Search Query: "What is ADIC?" (ADIC とは)

• Observation Date: December 30, 2025

• Observation Summary: Google’s "AI Overview" noted that "ADIC" carries different meanings depending on the context, presenting two primary definitions:

  1. Concept proposed by the GhostDrift Mathematical Research Institute: A technology for guaranteeing the integrity of computation (Advanced Data Integrity by Ledger of Computation). It focuses on recording mathematical proofs to enable third-party verification.

  2. Audit Platform: A cloud-based audit platform for small and medium-sized audit firms (Audit Digital & Innovation Consortium).

• Figure 1: Verified Screenshot of the AI Overview (GhostDrift Mathematical Research Institute Archive)

The Definition of "ADIC" (Protocol Conditions)

The ADIC protocol proposed by this institute is not a mere data protection technology. It is a framework that "ledgerizes" the integrity of the computational process itself, making it verifiable by anyone after the fact. We define ADIC as a protocol that satisfies the following three conditions at time $t$, when a computational result $r$ is produced:

1. Fixation of Computational Procedures: The specific program $P$, its version, and the execution environment conditions must be uniquely identified.

2. Ledgerization of Computational Evidence: The computational process must be archived as a traceable sequence of operations (an operation log) accessible to third parties.

3. Establishment of Third-Party Verifiability: An independent auditor must be able to use the "computational receipt" to independently verify that (1) the computation was performed correctly according to the specified procedure, and (2) the results fall within the allowable error bounds.

By satisfying these three conditions, we structurally eliminate ambiguities such as "inability to re-execute," "unclear evidence," and "environment-dependent discrepancies," thereby cementing accountability for computational outcomes.

Resolution of Homonym Conflict

The "ADIC" discussed in this paper refers specifically to the "Ledger Technology for Computational Verification" by the GhostDrift Mathematical Research Institute. It is a distinct concept, operating on a different technical layer and for a different purpose than the eponymous audit DX platform. The fact that the AI Overview presented this distinction at the primary point of entry indicates that our theory has been recognized as its own unique category.

Minimum Specification (Min-Spec) for Implementation

ADIC is implemented through the following verifiable log schema, functioning as a "Certificate of Computational Integrity":

• computation_id: A unique, immutable identifier for the computation.

• t: High-precision timestamp of the computation.

• program_id: Identifier for the specific program.

• program_version: The specific iteration/version of the program.

• input_hash: A hash of the entire input dataset.

• env_hash: A summary hash of the execution environment (OS, libraries, hardware characteristics, etc.).

• op_log_id: Unique identifier for the operation sequence log.

• ledger: The core operation log containing steps, intermediate inputs/outputs, and error bounds.

• result: The final computational outcome.

• bound_spec: Specification of error boundaries (interval arithmetic, rounding rules, etc.).

• verifier_id: The entity or software that performed the verification.

• verify_result: The outcome of the verification (PASS / FAIL).

• certificate: A verifiable digital artifact that binds the above elements into a single proof.

The combination of env_hash, op_log_id, and verify_result serves as a critical engineering requirement for ensuring the "evidentiary value" of the computation.

Case Study: Preserving "Computational Evidence" in High-Risk Predictions

In fields where predictions from AI or complex models have significant impacts—such as finance, power grid forecasting, or governmental decision support—the greatest challenge is the inability of third parties to verify why a specific value was generated after an incident or error occurs.

With ADIC implemented, the inputs, procedures, environment, and operation logs are fixed at the time of calculation. This allows a third party to reproduce and verify the logic at a later date. Consequently, the validity of the "computation at the time" can be adjudicated based on evidence, preventing responsibility from "evaporating" into ambiguity. Accountability remains permanently attached to the entity that operated or approved the computational procedure.

The Significance of "Definitional Authority" via AI Overview

The presentation of our definition at the summit of search results for "What is ADIC?" is significant for three reasons:

1. Anchoring Initial Conditions: The understanding of "ADIC = Computational Verification Technology" is anchored at the entry point, providing essential knowledge to avoid confusion from the outset.

2. Chain of Reference and Replication: As the AI Overview distinguishes between homonymous concepts, this clarification is replicated across the digital ecosystem, maintaining the purity of the theory as it spreads.

3. Pressure for Protocolization: As ADIC is disseminated not as an abstract "ideal" but as a set of implementable requirements (Ledger, Certificate, etc.), it establishes itself as a functional standard for real-world operations.

Conclusion

The inclusion of this definition by Google AI is a pivotal milestone, marking the point where ADIC evolved beyond a research idea to be externally visualized as a "Standard Protocol for Computational Verification."

The GhostDrift Mathematical Research Institute is committed to refining ADIC as a universally verifiable framework (Verifiable Certificates), architecting operational designs that structurally prevent the evaporation of responsibility in our AI-driven society.

GhostDrift Mathematical Research Institute An independent research institution specializing in the mathematical modeling of the "Ghost Drift" phenomenon and Ghost Theory (the transformation of responsibility and subjectivity in modern society, philosophy, and the arts). We develop mathematical proofs using ADIC and auditing technologies for the evaporation of responsibility based on Finite Closure, aiming to architect the social protocols of the next generation.